Home
Random
Log in
Settings
Donations
About Wikibooks
Disclaimers
Search
0.999.../Proof from 0.333...
Language
Watch
Edit
<
0.999...
Assumptions
edit
Decimal long division
Decimal multiplication by a small number
Proof
edit
Using long division,
${\frac {1}{3}}=0.333...$
Multiplying both sides by 3, we have
${\frac {3}{3}}=0.999...$
and therefore...
$1=0.999...$